Related papers: The Exact Renormalization Group and Approximations
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
We briefly review how it is possible to derive some exact expressions for the renormalization constants for the MS-like renormalization prescriptions using the arguments based on the renormalization group. These expressions are obtained for…
The coarse-graining operation in hydrodynamics is equivalent to a change of scale which can be formalized as a renormalization group transformation. In particular, its application to the probability distribution of a self-gravitating fluid…
We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional…
We study exact renormalisation group flows for background field dependent regularisations. It is shown that proper-time flows are approximations to exact background field flows for a specific class of regulators. We clarify the role of the…
We overview the entire renormalization theory, both perturbative and non-perturbative, by the method of the exact renormalization group (ERG). We emphasize particularly on the perturbative application of the ERG to the phi4 theory and QED…
In active matter systems, non-Gaussian, exact scaling exponents have been claimed in a range of systems using perturbative renormalization group (RG) methods. This is unusual compared to equilibrium systems where non-Gaussian exponents can…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form $-{\rm div}(a\nabla u)=f$ where $a=\exp(b)$ and $b$ is a Gaussian random field. The approximant of the solution $u$ is an…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
Tools for calculating the Renormalization Group Equations for renormalizable and non-renormalizable operators in various theories are reviewed, which are essential for comparing experimental results with predictions from models beyond the…
The renormalization-group (RG) functions for the three-dimensional n-vector cubic model are calculated in the five-loop approximation. High-precision numerical estimates for the asymptotic critical exponents of the three-dimensional impure…
The functional renormalisation group for the Einstein-Hilbert action is investigated for the case of four infinite (or large) and one compact dimension. The motivation for this study is given by the suggestion that gravity in more than four…
A method is introduced for approximate marginal likelihood inference via adaptive Gaussian quadrature in mixed models with a single grouping factor. The core technical contribution is an algorithm for computing the exact gradient of the…
The exact renormalization group (RG) method initiated by Wilson and further developed by Polchinski is used to study the shear flow model proposed by Avellaneda and Majda as a simplified model for the diffusive transport of a passive scalar…
We report an improved implementation for evaluating the analytical gradients of the random phase approximation (RPA) electron-correlation energy based on atomic orbitals and the localized resolution of identity scheme. The more efficient…
Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods…
Techniques based on $n$-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
We study the optimisation of exact renormalisation group (ERG) flows. We explain why the convergence of approximate solutions towards the physical theory is optimised by appropriate choices of the regularisation. We consider specific…